We use diagnostic tests all the time to determine whether someone has a disease or not,

both in research and in our everyday lives.

Quite often, we take results at face value.

But similar to our judgment,

diagnostic tests are not perfect.

This module is about the measures that quantify this imperfection.

The first two of these measures that I'm introducing to

you are sensitivity and specificity.

Let's consider Mary, a 50-year-old woman who would like to know if she has breast cancer.

The only way to be absolutely certain about

the diagnosis is to perform a meticulous autopsy on Mary.

But obviously, this is not a very practical method,

and our diagnosis would be of little use to Mary if she's not alive anymore.

Autopsy, in this case,

is called the gold standard test for the diagnosis of breast cancer.

But gold standard tests are often difficult to perform or very expensive.

In reality, the gold standard test for the diagnosis of breast cancer is a biopsy.

But even biopsies are costly,

invasive, and not without risks.

Therefore, the first step for Mary would be to do a mammography,

an imperfect but less invasive

tests which can potentially help us reach the correct diagnosis.

Although mammography can be inconclusive sometimes,

let's consider that there are two potential outcomes of a diagnostic test,

either positive, which indicates that the person has breast cancer,

or negative, which indicates that the person does not have the disease.

Let's say that Mary indeed has breast cancer when she undertakes mammography.

She could be correctly diagnosed as having the disease,

in which case, we say that we have a true positive result.

But she might receive a negative test result,

in which case, we would have a false negative result.

Similarly, if Mary does not have the disease but receives a positive test result,

we speak of a false positive result.

Finally, if Mary does not have cancer and receives a negative result,

we speak of a true negative result.

If you know the true disease status as defined by

the gold standard test and the test results of a number of people,

you can calculate the sensitivity and the specificity of this test.

Sensitivity is defined as the proportion of those with the disease who tested positive.

In other words, the proportion of

the true positive results among all individuals with the disease.

Specificity is defined as

the proportion of those without the disease who tested negative.

Alternatively, the proportion of

true negative results among all those without the disease.

Note that for both sensitivity and specificity,

the denominator is the disease state,

having the disease or not.

These two metrics are typically used to describe a diagnostic method because they're

specific to the method and their values don't depend on how frequent the disease is.

Sensitivity and specificity quantify

the misclassification observed in the diagnostic process,

and can be very useful when evaluating the effectiveness of a diagnostic test.